/INTER/TYPE5

Description

See main limitations of this interface in Comment 1.

Format

Definitions

Flags for Deactivation of Boundary Conditions: IBC

Definitions

Comments

1. The main limitations for this interface are:
   • The main segment normals must be oriented from main surface to the secondary nodes;
   • On the main side, the segments must be connected to solid or shell elements;
   • The same node may not be put in the two impact surfaces;
   • Some search problems (see Common Problems in the Radioss Theory Manual).
2. All the normals of the main surface segments must be oriented toward the secondary surface. Otherwise, mixing the orientation of the normals can lead to initial penetrations.
3. Secondary and main surfaces should be topologically different: a node cannot be on the two surfaces at the same time.
4. Flag I_del =1 has a CPU cost higher than I_del =2.
5. If the stiffness on the main side is much less than the stiffness on the secondary side, the stiffness factor Stfac can be increased to a value greater than 1; otherwise the stiffness factor should have a value between 0 and 1.
6. For example, the interface stiffness balance is:(1)
   $$\mathit{Stfac}\le \frac{E_s\cdot e_s}{E_m\cdot e_m}$$
   Where,

   $E_m$

   Main stiffness

   $e_m$

   Main thickness

   $E_s$

   Secondary stiffness

   $e_s$

   Secondary thickness

7. If I_BCX = 1, the boundary condition in X direction is deactivated. I_BCY and I_BCZ behave the same way respectively in Y and Z direction.
8. Boundary conditions are only deactivated on secondary nodes.
9. For friction formulation:
   • If the friction flag I_fric > 0 (default), the old static friction formulation is used:

     $F_T\le \mu \cdot F_N$ with $\mu =\mathit{Fric}$ (Coulomb friction).

   • If the friction flag I_fric > 0, new friction models are introduced. In this case, the friction coefficient is set by a function:(2)
     $$\mu =\text{μ}\left(p,V\right)$$
     Where,

     $p$

     Pressure of the normal force on the main segment

     $V$

     Tangential velocity of the secondary node relative to the main segment

   Currently, the following formulations are available:

   • I_fric = 1 (Generalized viscous friction law):
     (3)

     $$\mu =\mathit{Fric}+C_1.p+C_2\cdot V+C_3.p\cdot V+C_4\cdot p^2+C_5\cdot V^2$$
   • I_fric = 2 (Modified Darmstad law):(4)
     $$\mu =Fric+C_1\cdot e^{\left(C_{2}V\right)}\cdot p^2+C_3\cdot e^{\left(C_{4}V\right)}\cdot p+C_5\cdot e^{\left(C_{6}V\right)}$$
   • I_fric = 3 (Renard law):(5)
     $$\mu =C_1+\left(C_3-C_1\right)\cdot \frac{V}{C_5}\cdot \left(2-\frac{V}{C_5}\right)$$
     if $V\in \left[0,C_5\right]$ (6)

     $$\mu =C_3-\left(\left(C_3-C_4\right)\cdot {\left(\frac{V-C_5}{C_6-C_5}\right)}^2\cdot \left(3-2\cdot \frac{V-C_5}{C_6-C_5}\right)\right)$$
     if $V\in \left[C_5,C_6\right]$ (7)

     $$\mu =C_2-\frac{1}{\frac{1}{C_2-C_4}+{\left(V-C_6\right)}^2}$$

     if $V\ge C_6$

     Where,

     $C_1={\mu }_s$

     $C_2={\mu }_d$

     $C_3={\mu }_{\max }$

     $C_4={\mu }_{\min }$

     $C_5=V_{cr1}$

     $C_6=V_{cr2}$

   First critical velocity $V_{cr1}=C_5$ must be different to 0 ( $C_5\ne 0$ ).

   First critical velocity $V_{cr1}=C_5$ must be less than the second critical velocity $V_{\mathit{cr}2}=C_6(C_5<C_6)$ .

   The static friction coefficient C₁ and the dynamic friction coefficient C₂, must be less than the maximum friction C₃ ( $C_1\le C_3$ and $C_2\le C_3$ ).

   The minimum friction coefficient C₄ must be less than the static friction coefficient C₁ and the dynamic friction coefficient C₂ ( $C_4\le C_1$ and $C_4\le C_2$ ).

   Table 1. Units for Friction Formulations

   Ifric	Fric	C1	C2	C3	C4	C5	C6
   1		$\left[\frac{1}{\text{P}\text{a}}\right]$	$\left[\frac{\text{s}}{\text{m}}\right]$	$\left[\frac{\text{s}}{\text{Pa}\cdot \text{m}}\right]$	$\left[\frac{1}{{\text{Pa}}^2}\right]$	$\left[\frac{{\text{s}}^2}{{\text{m}}^2}\right]$
   2			$\left[\frac{\text{s}}{\text{m}}\right]$		$\left[\frac{\text{s}}{\text{m}}\right]$		$\left[\frac{\text{s}}{\text{m}}\right]$
   3						$\left[\frac{\text{m}}{\text{s}}\right]$	$\left[\frac{\text{m}}{\text{s}}\right]$

10. If I_filtr flag is not zero, the tangential forces are smoothed using a filter:(8)
    $$F_T=\alpha \cdot {F^{\prime }}_T+\left(1-\alpha \right)\cdot {{F^{\prime }}_T}^{-1}$$

    Where, α coefficient is calculated from:

    if I_filtr =1 ➤ $\alpha =X_{freq}$ , simple numerical filter

    if I_filtr =2 ➤ $\alpha =\frac{2\cdot \pi }{X_{freq}}$ , standard -3dB filter, with $X_{freq}=\frac{dt}{T}$ , and T = filtering period

    if I_filtr =3 ➤ $\alpha =2\cdot \pi \cdot X_{freq}\cdot dt$ standard -3dB filter, with X_freq = cutting frequency

11. The coefficients C₁ through C₆ are used to define a variable friction coefficient $\mu$ for new friction formulations.
12. Since the coordinate change will be irreversible, this action needs be made with great precaution because it may:
    • Create other initial penetrations, if several surface layers are defined in the interfaces
    • Create initial energy if node belongs to spring element

    Inacti = 3 or 4 is only recommended for small initial penetrations.

13. In 2D analysis, tangent contact force is limited when $P_{tlim}$ is defined by the following equation:(9)
    $$F_t\le P_{tlim}\frac{S}{\sqrt{3}}$$

    While, $S$ is extrapolated length of segments connected to the secondary node.